The Argentine failed to score for the second straight game but provided two assists to play an important role in their victory.
Numerous celebrities were in attendance at the BMO Stadium, including Selena Gomez, Leonardo DiCaprio Tom Holland and Toby Maguire.
LAFC were the better side in the first-half and created several goal-scoring opportunities but their lack of finishing let them down.
The Herons’ 14th-minute goal came against the run of play when Facundo Farías scored with a sliding finish, with Tomás Avilés the provider.
Messi almost added another after a smart lay-off from Diego Gómez, but John McCarthy made a superb save to deny the visitors.
Miami doubled their advantage soon after the break with Messi at the centre of it again.
The 36-year-old found Jordi Alba sprinting down the left wing and his former Barcelona calmly slotted past the keeper.
The Argentine delivered another excellent assist late in the game as he set up Leonardo Campana for Inter’s third goal.
Ryan Hollingshead pulled one back but that was small consolation for the reigning MLS champions, who slumped to a 3-1 defeat.
The latest victory leaves the Herons eight points behind ninth-place DC United in the MLS Eastern Conference play-off race.
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